I have long thought but I think there is no way to make this German idiom in Italian, at least, not literally.

To make the right sense, you could translate “L’alcool è il rimedio per districare il groviglio che hai in testa” and it’s clear enough, but in this case there is no reference to salad or to dressing.

Actually you can translate “Dressing” in Italian as “lavata” or “condimento” (maybe also “medicamento”, “rimedio”).
And indeed you can say “lavata di capo” but with a different meaning: it’s a harsh rebuke to clean up the mind of someone who did something wrong.

Or else, with a cooking reference, you could say “il condimento per il minestrone che hai in testa” but it’s a metaphor not immediately comprehensible as it is in German.
Another Italian idiom is “come il cacio sui maccheroni”, which also refers to cooking. Cheese is the most common condiment for pasta, it fits perfectly:
“L’alcool è come il cacio sui maccheroni per la tua testa scombussolata”.
Anyway, this is also a bit too elaborate and hasn’t the same spontaneity of the German idiom.

So, you can choose what you prefer, a free translation or a more literal but less fitting translation.